Searching for non-Kerr objects

Abstract

We suggest a method that could be used to discriminate a Kerr black hole from any other supermassive axisymmetric astrophysical object by analyzing the gravitational-wave signal from an extreme mass ratio inspiral (EMRI). The method is based on the quite distinct qualitative features that characterize a slightly nonintegrable system. According to the Poincaré-Birkhoff theorem, whenever a resonance of frequencies arise in an axisymmetric perturbed Kerr metric, instead of the anticipated KAM curves of the integrable Kerr case, a Birkhoff chain of islands appears on a surface of sections. The orbits of this chain of islands have a fixed ratio of frequencies. The idea is to exploit this feature to check if the inspiraling low-mass object spends a finite interval of time to cross this resonance, while its orbit evolves adiabatically due to the radiation of gravitational waves.